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2014 Total Positivity of the Cubic Trigonometric Bézier Basis
Xuli Han, Yuanpeng Zhu
J. Appl. Math. 2014: 1-5 (2014). DOI: 10.1155/2014/198745

Abstract

Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters λ and μ given in Han et al. (2009) forms an optimal normalized totally positive basis for λ,μ∈(-2,1]. Moreover, we show that for λ=-2 or μ=-2 the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.

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Xuli Han. Yuanpeng Zhu. "Total Positivity of the Cubic Trigonometric Bézier Basis." J. Appl. Math. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/198745

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010568
MathSciNet: MR3187034
Digital Object Identifier: 10.1155/2014/198745

Rights: Copyright © 2014 Hindawi

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